The background art of the first aspect of the present invention will first be described below.
An inverter device having a variable fundamental AC frequency generally produces an output signal of rectangular wave according to pulse width modulation (PWM). Since rectangular waves contain many harmonic components, they tend to give rise to noise. One proposal to solve such a problem has been a system for outputting a sine wave by rounding the corners of a rectangular wave to get rid of harmonic components. For outputting such a sine wave, it has been practiced to extract only harmonic components with a usual highpass filter using real coefficients and feed back the extracted harmonic components. However, because the highpass filter allows a low-frequency fundamental component to be fed back without being fully removed, and also because the difference between high and low frequencies is reduced as the frequency of the fundamental component rises, it is difficult to remove the low-frequency fundamental component, resulting in a reduction in inverter device performance.
Conventional systems using filters represented by transfer functions using real coefficients find it difficult to separate two close resonant frequencies of the same sign and also resonant frequencies of opposite signs (+, -) whose absolute values are equal or very close to each other. For example, there is an instance where there are two resonant modes of opposite signs whose absolute are very close to each other. In such an instance, one of the modes is to be left untouched because sufficient attenuation has been given thereto for some reasons, but the remaining mode needs to be selected if it is unstable. The above conventional filters fail to select the remaining mode only, but control both the modes simultaneously, with result that the mode to be left intact may be adversely affected.
One filter for eliminating the above drawback is known as a tracking filter. With such a tracking filter, a rotating coordinate system is assumed by rotating a stationary coordinate system at the angular velocity of its mode, and, as viewed from the rotating coordinate system, the angular velocity component is equivalent to a DC component because its frequency is zero. The DC component is separated by a highpass filter or a lowpass filter, and transformed back into the stationary coordinate system. Since this filter is required not to separate a certain AC component from a plurality of AC components, but to separate only a DC component transformed into the rotating coordinate system, it is quite easy to separate the DC component with a highpass filter or a lowpass filter.
In an apparatus for controlling the above inverter device, it has been proposed to regard a fundamental component as a DC component by way of coordinate transformation from the stationary coordinate system into the rotating coordinate system, remove the DC component with a highpass filter, and transform only harmonic components back into the stationary coordinate system so as to feed them back.
Specifically, FIG. 16 shows by way of example a control apparatus for an inverter device for outputting a sine wave. An AC electric power having a commercial voltage and frequency is supplied from a commercial three-phase AC power supply 11 to an inverter device 12, which outputs and supplies an AC electric power having an arbitrary voltage and frequency to a load 13 according to a command from a pulse width modulation circuit 15. A resonant circuit 14 removes high-frequency components from a pulse-width-modulated rectangular wave outputted from the inverter device 12, thus generating a voltage waveform close to a sine wave. The output voltage waveform supplied to the load 13 is converted by a three-phase-to-two-phase converter 17 into an orthogonal two-axis signal, which is then transformed from a stationary coordinate system into a rotating coordinate system by a coordinate transformation circuit 18. The coordinate transformation is effected by calculating a matrix C. Since the transformed signal has a DC fundamental component, the DC fundamental component is removed by a highpass filter 19, and the signal is multiplied by a gain K by a calculating circuit 20. The signal is then transformed back into the stationary coordinate system by a coordinate transformation circuit 21 which calculates a matrix C.sup.-1. The transformed signal is converted into a three-phase signal by a two-phase-to-three-phase converter 22. The three-phase signal is subtracted from a signal from a fundamental signal generator 16 by an adder 23, and hence is fed back to the input of the inverter device.
It is well known to design and analyze speed control circuits for inverter devices associated with motors, synchronous machines, etc. by transforming signal components into orthogonal coordinates referred to as d-q coordinates or .gamma.-.delta. coordinates. According to the present invention, as described later on, no consideration at all is given to filter circuits using complex coefficient transfer functions as two-input/two-output systems, and applications of complex gains.
In the above example of the apparatus for controlling inverter device, since the fundamental is AC, the rotational angle of the rotating coordinate system is not constant or stationary, and the rotating coordinate system keeps rotating. For coordinate transformation, therefore, as shown in FIG. 16, there is required a matrix calculating circuit, i.e., a resolver circuit, for generating at all times sine and cosine waves of the rotational angle of the rotating coordinate system as time functions, multiplying two input signals by the generated sine and cosine waves, separating and combining their vectors. Since inverse transformation into the original stationary coordinate system is needed, two such resolver circuits are necessary. If they are constructed as analog circuits, then many hardware components will be required, resulting in a complex circuit arrangement. If they are constructed as digital circuits, then the time required for necessary calculations will be long.
According to the above conventional process, it has been impossible to adjust the phase of an orthogonal two-axis signal to an arbitrary value irrespective of the frequency as with the gain. Furthermore, it has heretofore been impossible to change the phase sharply by .+-.180.degree. during a certain angular frequency.
The background of the single-input single-output filter circuit for use in communication, control, etc. according to the second aspect of the present invention will be described below.
Filter circuits for use in various forms of communication, control, etc. have heretofore been designed and constructed on the basis of transfer functions using real coefficients. With conventional lowpass or highpass filters, no distinction is made between positive and negative values of the angular frequency .OMEGA. of signals. If the negative frequency range is covered, then the conventional lowpass or highpass filters have symmetrical gain characteristics with respect to the origin, i.e., the zero frequency. This means that the conventional lowpass or highpass filters have been used as a bandpass or bandstop filter whose central frequency is zero. Therefore, as shown in FIG. 19, as corner angular frequencies (a, b) are higher, the bandwidth is greater. It is difficult to obtain highly steep gain characteristics when the horizontal coordinates are represented on a linear scale, but not a logarithmic scale log .OMEGA., of the angular frequency.
This can easily be understood from the fact that while the gradient (dB/dec) of an approximating broken line of the gain characteristic of an ordinary Bode diagram remains the same in any frequency ranges, a change (increase) in the frequency, not logarithmic, represented by horizontal coordinates is much greater as the corner frequency is higher. For example, changes per 1 dec. in corner frequencies 10 and 1000 are 100-10=90 and 10000-1000=9000, respectively, and the former is 100 times steeper than the latter on the linear scale though they are of the same gradient in a Bode diagram.
A biquad filter is known as a filter using a conventional resonant circuit of real coefficients. The biquad filter comprises two integrating circuits connected into a feedback loop. While the biquad filter provides a bandpass filter having a relatively narrow bandwidth, it is problematic in that it is difficult to control the steepness of the filter if the resonant frequency .omega. is variable.
The control of a high-speed rotating body requires a filter circuit for passing or stopping a narrow bandwidth in the vicinity of the rotational speed of the rotating body. It has been the conventional practice to achieve the steep characteristic of such a narrow band filter by transforming coordinates from the stationary coordinate system into the rotating coordinate system and replacing the rotational speed with zero. Specifically, an input signal in the stationary coordinate system is multiplied by a sine or cosine function so as to be transformed into the rotating coordinate system. Then, a rotationally synchronized signal component is removed by a lowpass filter, leaving only a frequency component in a narrow band, which needs to be transformed back into the stationary coordinate system. Therefore, it has been necessary to prepare, in addition to the lowpass filter, two coordinate transformation circuits by generating sine and cosine functions corresponding to the rotational speed of the rotating body.
With the above conventional process, it is impossible to adjust a phase to an arbitrary value irrespective of the frequency as with the gain.
For the control of a rotating body, since it is controlled from radial orthogonal two axes, it is often customary to use real numbers for signals related to the x-axis and complex variables with imaginary numbers multiplied by j for signals related to the y-axis. Transfer functions including complex numbers are highly effective analytical means for such an application. For such transfer functions including complex numbers, a distinction should be made between positive and negative values of the frequency, and characteristic roots of a system do not necessarily become conjugate roots.
For example, a first-order lowpass filter k/(a+s) has a corner angular frequency "a" and a central angular frequency which is zero. Therefore, in a complex system, if the central angular frequency is not limited to zero, but is .omega., for example, then k/{a+(s-j.omega.)} changes to a complex coefficient transfer function. At the same time, "a" represents the distance from .omega., not from zero, or half the passband. Inasmuch as .omega., even though it is of a high value, is returned to the origin, if .omega. is selected to be 1000 and "a" is selected to be 10, the gradient of the broken line is about 100 times steeper than the case of .omega.=0 on the logarithmic scale, and (.omega.-a) on the opposite side of .omega. is also represented by a broken line, resulting in a narrow steep bandpass characteristic.
However, since the filter circuits using complex coefficients for two-input/two-output systems handle variables on spatially orthogonal x- and y-axes as complex numbers, they cannot be used directly for communication/control for single-input single-output systems.